It is known that some of the conventional power transmissions are arranged in a manner that downshift during a relatively high vehicle speed is achieved only when the accelerator pedal is continuously depressed to its full extent. However, in this case, the following drawbacks will inevitably arise: since the downshift is established by the continuous full depression of the accelerator pedal, it will induce wasteful fuel consumption of the engine. Furthermore, if the accelerator pedal is abruptly released from its fully depressed position, upshift takes place suddenly. This is very undesirable in case rapid acceleration of the vehicle is required.